Spatio-Temporal Pattern Formation
Spatio-Temporal Pattern Formation

Author: Daniel Walgraef

Publisher: Springer

Published: 1996-12-13

Total Pages: 0

ISBN-13: 9780387948577

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Spatio-temporal patterns appear almost everywhere in nature, and their description and understanding still raise important and basic questions. However, if one looks back 20 or 30 years, definite progress has been made in the modeling of insta bilities, analysis of the dynamics in their vicinity, pattern formation and stability, quantitative experimental and numerical analysis of patterns, and so on. Universal behaviors of complex systems close to instabilities have been determined, leading to the wide interdisciplinarity of a field that is now referred to as nonlinear science or science of complexity, and in which initial concepts of dissipative structures or synergetics are deeply rooted. In pioneering domains related to hydrodynamics or chemical instabilities, the interactions between experimentalists and theoreticians, sometimes on a daily basis, have been a key to progress. Everyone in the field praises the role played by the interactions and permanent feedbacks between ex perimental, numerical, and analytical studies in the achievements obtained during these years. Many aspects of convective patterns in normal fluids, binary mixtures or liquid crystals are now understood and described in this framework. The generic pres ence of defects in extended systems is now well established and has induced new developments in the physics of laser with large Fresnel numbers. Last but not least, almost 40 years after his celebrated paper, Turing structures have finally been ob tained in real-life chemical reactors, triggering anew intense activity in the field of reaction-diffusion systems.

On Growth and Form
On Growth and Form

Author: M. A. J. Chaplain

Publisher: John Wiley & Sons

Published: 1999

Total Pages: 448

ISBN-13:

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On Growth and Form Spatio-temporal Pattern Formation in Biology M. A. J. Chaplain and G. D. Singh, both of the University of Dundee, UK J. C. McLachlan, St. Andrews University, UK Spatio-temporal pattern formation is a major area of research within the subject of mathematical biology. The topic involves the use of mathematical modelling to analyse how patterns in biology are created and develop. For example, the growth, over time, of the intricate and beautiful patterns on certain sea-shells or the striped markings on a tiger can be modelled and their development predicted in terms of non-linear mathematical processes. The current volume captures the breadth of recent research into various aspects of spatio-temporal pattern and form, such as development biology, reaction-diffusion systems and morphometrics. * Brings the ideas of the classic On Growth and Form by D'Arcy Thompson, the founding classic of mathematical biology, fully up to date and looks to future developments in the subject * Foreword provided by Professor John Tyler Bonner, Princeton University * World class collection of internationally renowned contributors from both experimental and theoretical backgrounds Taking its inspiration from D'Arcy Thompson's classic and still influential volume On Growth and Form, this new volume presents a collection of 21 articles from the Plenary Speakers of the recent D'Arcy Thompson Conference, held at the University of Dundee, 20-24 September 1998. The topics covered include pattern formation in development biology, reaction-diffusion systems, intercellular systems and morphometrics, offering the reader a stimulating blend of theory and experiment. This book will be of particular interest to bio-mathematicians and development biologists. Paediatric clinicians, evolutionary biologists, orthodontists, anatomists, physiologists and many other members of the biology community will also benefit greatly from it.

Spatio-Temporal Pattern Formation
Spatio-Temporal Pattern Formation

Author: Daniel Walgraef

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 310

ISBN-13: 1461218500

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Spatio-temporal patterns appear almost everywhere in nature, and their description and understanding still raise important and basic questions. However, if one looks back 20 or 30 years, definite progress has been made in the modeling of insta bilities, analysis of the dynamics in their vicinity, pattern formation and stability, quantitative experimental and numerical analysis of patterns, and so on. Universal behaviors of complex systems close to instabilities have been determined, leading to the wide interdisciplinarity of a field that is now referred to as nonlinear science or science of complexity, and in which initial concepts of dissipative structures or synergetics are deeply rooted. In pioneering domains related to hydrodynamics or chemical instabilities, the interactions between experimentalists and theoreticians, sometimes on a daily basis, have been a key to progress. Everyone in the field praises the role played by the interactions and permanent feedbacks between ex perimental, numerical, and analytical studies in the achievements obtained during these years. Many aspects of convective patterns in normal fluids, binary mixtures or liquid crystals are now understood and described in this framework. The generic pres ence of defects in extended systems is now well established and has induced new developments in the physics of laser with large Fresnel numbers. Last but not least, almost 40 years after his celebrated paper, Turing structures have finally been ob tained in real-life chemical reactors, triggering anew intense activity in the field of reaction-diffusion systems.

Numerically Solving Polynomial Systems with Bertini
Numerically Solving Polynomial Systems with Bertini

Author: Daniel J. Bates

Publisher: SIAM

Published: 2013-11-08

Total Pages: 372

ISBN-13: 1611972698

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This book is a guide to concepts and practice in numerical algebraic geometry ? the solution of systems of polynomial equations by numerical methods. Through numerous examples, the authors show how to apply the well-received and widely used open-source Bertini software package to compute solutions, including a detailed manual on syntax and usage options. The authors also maintain a complementary web page where readers can find supplementary materials and Bertini input files. Numerically Solving Polynomial Systems with Bertini approaches numerical algebraic geometry from a user's point of view with numerous examples of how Bertini is applicable to polynomial systems. It treats the fundamental task of solving a given polynomial system and describes the latest advances in the field, including algorithms for intersecting and projecting algebraic sets, methods for treating singular sets, the nascent field of real numerical algebraic geometry, and applications to large polynomial systems arising from differential equations. Those who wish to solve polynomial systems can start gently by finding isolated solutions to small systems, advance rapidly to using algorithms for finding positive-dimensional solution sets (curves, surfaces, etc.), and learn how to use parallel computers on large problems. These techniques are of interest to engineers and scientists in fields where polynomial equations arise, including robotics, control theory, economics, physics, numerical PDEs, and computational chemistry.

Cellular Automaton Modeling of Biological Pattern Formation
Cellular Automaton Modeling of Biological Pattern Formation

Author: Andreas Deutsch

Publisher: Birkhäuser

Published: 2018-03-09

Total Pages: 470

ISBN-13: 1489979808

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This text explores the use of cellular automata in modeling pattern formation in biological systems. It describes several mathematical modeling approaches utilizing cellular automata that can be used to study the dynamics of interacting cell systems both in simulation and in practice. New in this edition are chapters covering cell migration, tissue development, and cancer dynamics, as well as updated references and new research topic suggestions that reflect the rapid development of the field. The book begins with an introduction to pattern-forming principles in biology and the various mathematical modeling techniques that can be used to analyze them. Cellular automaton models are then discussed in detail for different types of cellular processes and interactions, including random movement, cell migration, adhesive cell interaction, alignment and cellular swarming, growth processes, pigment cell pattern formation, tissue development, tumor growth and invasion, and Turing-type patterns and excitable media. In the final chapter, the authors critically discuss possibilities and limitations of the cellular automaton approach in modeling various biological applications, along with future research directions. Suggestions for research projects are provided throughout the book to encourage additional engagement with the material, and an accompanying simulator is available for readers to perform their own simulations on several of the models covered in the text. QR codes are included within the text for easy access to the simulator. With its accessible presentation and interdisciplinary approach, Cellular Automaton Modeling of Biological Pattern Formation is suitable for graduate and advanced undergraduate students in mathematical biology, biological modeling, and biological computing. It will also be a valuable resource for researchers and practitioners in applied mathematics, mathematical biology, computational physics, bioengineering, and computer science. PRAISE FOR THE FIRST EDITION “An ideal guide for someone with a mathematical or physical background to start exploring biological modelling. Importantly, it will also serve as an excellent guide for experienced modellers to innovate and improve their methodologies for analysing simulation results.” —Mathematical Reviews

Mathematical Models for Biological Pattern Formation
Mathematical Models for Biological Pattern Formation

Author: Philip K. Maini

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 327

ISBN-13: 1461301335

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This 121st IMA volume, entitled MATHEMATICAL MODELS FOR BIOLOGICAL PATTERN FORMATION is the first of a new series called FRONTIERS IN APPLICATION OF MATHEMATICS. The FRONTIERS volumes are motivated by IMA pro grams and workshops, but are specially planned and written to provide an entree to and assessment of exciting new areas for the application of mathematical tools and analysis. The emphasis in FRONTIERS volumes is on surveys, exposition and outlook, to attract more mathematicians and other scientists to the study of these areas and to focus efforts on the most important issues, rather than papers on the most recent research results aimed at an audience of specialists. The present volume of peer-reviewed papers grew out of the 1998-99 IMA program on "Mathematics in Biology," in particular the Fall 1998 em phasis on "Theoretical Problems in Developmental Biology and Immunol ogy." During that period there were two workshops on Pattern Formation and Morphogenesis, organized by Professors Murray, Maini and Othmer. James Murray was one of the principal organizers for the entire year pro gram. I am very grateful to James Murray for providing an introduction, and to Philip Maini and Hans Othmer for their excellent work in planning and preparing this first FRONTIERS volume. I also take this opportunity to thank the National Science Foundation, whose financial support of the IMA made the Mathematics in Biology pro gram possible.

Runtime Verification
Runtime Verification

Author: Ezio Bartocci

Publisher: Springer

Published: 2015-09-19

Total Pages: 439

ISBN-13: 3319238205

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This book constitutes the refereed proceedings of the 6th International Conference on Runtime Verification, RV 2015, held in Vienna, Austria, in September 2015. The 15 revised full papers presented together with 4 short papers, 2 tool papers, 4 tutorials, 3 invited talks, and 2 software competition papers were carefully reviewed and selected from 45 submissions. The discussion of the conference centers around two main aspects. The first is to understand wether the runtime verification techniques can practically complement the traditional methods proving programs correct before their execution, such as model checking and theorem proving. The second concerns with formal methods and how their application can improve traditional ad-hoc monitoring techniques used in performance monitoring, hardware design emulation and simulation, etc.

Fractional Order Systems and Applications in Engineering
Fractional Order Systems and Applications in Engineering

Author: Dumitru Baleanu

Publisher: Academic Press

Published: 2022-11-17

Total Pages: 392

ISBN-13: 032390954X

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Fractional Order Systems and Applications in Engineering presents the use of fractional calculus (calculus of non-integer order) in the description and modelling of systems and in a range of control design and practical applications. The book covers the fundamentals of fractional calculus together with some analytical and numerical techniques, and provides MATLAB® codes for the simulation of fractional-order control (FOC) systems. The use of fractional calculus can improve and generalize well-established control methods and strategies. Many different FOC schemes are presented for control and dynamic systems problems. These extend to the challenging control engineering design problems of robust and nonlinear control. Practical material relating to a wide variety of applications including, among others, mechatronics, civil engineering, irrigation and water management, and biological systems is also provided. All the control schemes and applications are presented with either system simulation results or real experimental results, or both. Fractional Order Systems and Applications in Engineering introduces readers to the essentials of FOC and imbues them with a basic understanding of FOC concepts and methods. With this knowledge readers can extend their use of FOC in other industrial system applications, thereby expanding their range of disciplines by exploiting this versatile new set of control techniques. - Provides the most recent and up-to-date developments on the Fractional-order Systems and their analyzing process - Integrates recent advancements of modeling of real phenomena (on Fractional-order Systems) via different-different mathematical equations with demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering - Provides readers with illustrative examples of how to use the presented theories of Fractional-order Systems in specific cases with associated MATLAB code

Nonlinear Dynamics and Pattern Formation in the Natural Environment
Nonlinear Dynamics and Pattern Formation in the Natural Environment

Author: A. Van Harten

Publisher: Taylor & Francis

Published: 2022-09-16

Total Pages: 350

ISBN-13: 1351428268

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This Research Note aims to provide an insight into recent developments in the theory of pattern formation. In the last decade there has been considerable progress in this field, both from a theoretical and a practical point of view. Recent mathematical developments concern the study of the nonlinear stability of systems at near-critical conditions by an appropriate system of modulation equations. The complexity of the original problem can be reduced drastically by this approximation. Moreover, it provides unifying point of view for a wide range of problems. New applications of the theory arise in a multitude of scientific areas such as hydrodynamics, reaction-diffusion problems, oceanography, meteorology, combustion, geophysical and biological morphodynamics and semi-conductors.This book is intended to show the interactions between the mathematical theory of nonlinear dynamics and the study of pattern generating phenomena in the natural environment. There is an intimate relationship between new insights in the mathematical aspects of nonlinear pattern formation and the comprehension of such phenomena. Therefore there are two partly overlapping main themes: one in which the emphasis is on generally applicable mathematical theories and techniques and one in which the phenomenology of pattern evolution in various areas is discussed.The book comprises 19 contributions by experts in the field. Although the emphasis changes considerably from paper to paper, in each contribution the same two themes are present; all the authors have aimed to achieve a suitable balance between the mathematical theory and the physical phenomena.